Question

The sum of two numbers is 91. The smaller number is thirteen less than the larger number. Find both numbers.

a) 52, 39
b) 42, 49
c) 38, 53
d) 31, 60

Answer 1

To find the two numbers, set up a system of equations based on the given information. The larger number is 52 and the smaller number is 39.

Step-by-step explanation:

To find the two numbers, we can set up a system of equations based on the given information:

Let x be the larger number.

The smaller number is x-13.

We know that the sum of the two numbers is 91, so we can write the equation:

x + (x-13) = 91

Simplifying the equation gives:

2x - 13 = 91

Adding 13 to both sides gives:

2x = 104

Dividing both sides by 2 gives:

x = 52

So the larger number is 52. The smaller number can be found by subtracting 13:

52 - 13 = 39

Therefore, the two numbers are 52 and 39.